Answer
$(a)$. $$\frac{dy}{dx}=\frac{2}{y}$$
$(b)$. SLope of the tangent to the curve is $m=1$
Work Step by Step
$(a)$. Use implicit differentiation to find $\frac{dy}{dx}$ for $y^2=4x$
Taking the derivative implicitly we get:
$$2y\frac{dy}{dx}=4$$
Solve for $\frac{dy}{dx}$
$$\frac{dy}{dx}=\frac{4}{2y}=\frac{2}{y}$$
$(b)$. Finding slope of tangent line at the point $(1,2)$ for the above function.
We do this by plugging in the point $(1,2)$ into the derivative from part $(a)$. Hence:
$$\frac{dy}{dx}=\frac{2}{(2)}=1$$
